Pricing Longevity Bonds Using Affine-Jump Diffusion Models

Jorge Bravo

CEFAGE-UE Working Papers from University of Evora, CEFAGE-UE (Portugal)

Abstract: Historically, actuaries have been calculating premiums and mathematical reserves using a deterministic approach, by considering a deterministic mortality intensity, which is a function of the age only, extracted from available (static) life tables and by setting a flat ("best estimate") interest rate to discount cash flows over time. Since neither the mortality intensity nor interest rates are actually deterministic, life insurance companies and pension funds are exposed to both financial and mortality (systematic and unsystematic) risks when pricing and reserving for any kind of long-term living benefits, particularly on annuities and pensions. In this paper, we assume that an appropriate description of the demographic risks requires the use of stochastic models. In particular, we assume that the random evolution of the stochastic force of mortality of an individual can be modelled by using doubly stochastic processes. The model is then embedded into the well known affine-jump framework, widely used in the term structure literature, in order to derive closed-form solutions for the survival probability. We show that stochastic mortality models provide an adequate framework for the development of longevity risk hedging tools, namely mortality-linked contracts such as longevity bonds or mortality derivatives.

JEL-codes: G22 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2011
New Economics Papers: this item is included in nep-age
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:cfe:wpcefa:2011_29

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